The Semi-discrete Method for the Approximation of the Solution of Stochastic Differential Equations

Boundary preserving explicit scheme for the Aït-Sahalia mode

“…It seems that the proposed method still works, even if we exceed the boundaries suggested by the condition we have assumed for the parameters. In particular, for 2-strong convergence we require 7 2 (k 3 ) 2 ≤ k 2 . The moments of the original process are bounded when (k 3 ) 2 ≤ k 2 .…”

“…The model was proposed in [1] to study the spot interest rate and especially for the case r = 2. The numerical approximation of (1) was studied in [8] using an implicit scheme, in [6] again by applying an implicit method and in [3] using an explicit positivity preserving numerical scheme applying the semi-discrete method, see [2] for the original proposition of the method and [7] and references therein for a review of the method. The order of strong convergence of the proposed semi-discrete numerical scheme in [3] was not proved.…”